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Extreme singular values and eigenvalues of non-Hermitian block Toeplitz matrices

โœ Scribed by Stefano Serra Capizzano; Paolo Tilli

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
151 KB
Volume
108
Category
Article
ISSN
0377-0427

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๐Ÿ“œ SIMILAR VOLUMES

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โœ Stefano Serra ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 758 KB

We are concerned with the behavior of the minimum (maximum) eigenvalue A~0 "~ (A~ "~) of an (n + 1) X (n + 1) Hermitian Toeplitz matrix T~(f) where f is an integrable real-valued function. Kac, Murdoch, and Szeg5, Widom, Patter, and R. H. Chan obtained that A}~ 0 -rain f = O(1/n 2k) in the case whe

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โœ E.E. Tyrtyshnikov; N.L. Zamarashkin ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 230 KB

In contrast to the Hermitian case, the ``unfair behavior'' of non-Hermitian Toeplitz eigenvalues is still to be unravelled. We propose a general technique for this, which reveals the eigenvalue clusters for symbols from v I . Moreover, we study a thin structure of those clusters in the terms of prop